There is no doubt that Veera Rajendra's (Mr Srihari) works deserve our full praise and appreciation.
However the Kulasekhara - Rajasekara relationship needs to be relooked. Kulasekhara perumal was probably the first famous ruler of the perumal dynasty but other than the prabhanthams no historic trace of this famous king exists
Cheraman perumal was originally kazhatrarivar and was not related to kulasekhara - according to periyapuranam. He is chosen as king by the elephant
The very first perumal king historically proven is rajasekhara who issued vazappalli copper plates
Until further evidences present themselves, it is hard to connect these 3 kings